In their paper [1]}, Myasnikov, Nikolaev, and Ushakov started the investigation of classical
discrete optimization problems, which are classically formulated over the integers,
for arbitrary (possibly non-commutative) groups. The general goal of this line of research is to study
to what extent results from the classical commutative setting can be transferred to the non-commutative setting.
Among other problems, Myasnikov et al. introduced for a finitely generated group \(G\) 
the knapsack problem and the subset sum problem.
The input for the knapsack problem is a sequence of group elements \(g_1, \ldots , g_k, g \in G\)  (specified
by finite words over the generators of \(G\) ) and it is asked whether there exists a solution
\((x_1, \ldots , x_k) \in \mathbb {N}^k\) 
of the equation \(g_1^{x_1} \cdots g_k^{x_k} = g\) . For the subset sum problem one restricts the solution
to \(\lbrace 0,1\rbrace ^k\) .
